基于三机理模型的孔隙半径分布对页岩岩心表观渗透率的影响分析
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摘要
为了研究实际状态下页岩岩心中页岩气的表观渗透率及其变化规律,在考虑孔隙内壁的粗糙性、孔隙中的吸附层以及孔隙的弯曲程度的基础上,建立新的实际状态页岩气在单一孔隙中流动时的三机理表观渗透率模型。基于此模型,将岩心等效为不同半径的弯曲圆管束,建立页岩岩心中页岩气的表观渗透率模型,计算岩心中黏滞流、Knudsen扩散以及表面扩散对表观渗透率的贡献大小,分析不同孔隙半径分布和岩心中最大孔隙半径对表观渗透率的影响。结果表明:岩心中大孔隙对表观渗透率的影响远远大于小孔隙;随着最大孔隙半径的增加,不同孔隙分布之间的表观渗透率差异越来越小;低压下或低孔隙半径条件下,表面扩散对表观渗透率的影响不可忽略;油藏条件下,相对于Knudsen扩散和表面扩散,页岩岩心中的黏滞流对表观渗透率的贡献占主导地位,而表面扩散的影响可以忽略。
In order to study the apparent permeability and variation of shale gas in the core of shale rock under the actual state,a new three-mechanism apparent permeability model for the flow of shale gas in a single pore was established by taking the roughness of the inner wall,the adsorption layer in the pore and the bending degree of the pore into consideration. Based on this model,the apparent permeability model of shale gas in shale core was established by equatng the core to a curved circular bundle with different radius,and the contribution of viscous flow,Knudsen diffusion and surface diffusion to apparent permeability were calculated. The influence of the distribution of different pore radius and the maximum pore radius on the apparent permeability were analyzed. The results showed that the effect of macropore on apparent permeability was much greater than that of micropore in the core. With the increase of the maximum pore radius,the apparent permeability between different pore distributions became smaller and smaller. Under the condition of low pressure or low pore radius,the effect of surface diffusion on apparent permeability should not be neglected. Compared with Knudsen diffusion and surface diffusion,the contribution of viscous flow in the shale core to apparent permeability was dominant under reservoir conditions,and the influence of surface diffusion could be ignored.
In order to study the apparent permeability and variation of shale gas in the core of shale rock under the actual state,a new three-mechanism apparent permeability model for the flow of shale gas in a single pore was established by taking the roughness of the inner wall,the adsorption layer in the pore and the bending degree of the pore into consideration. Based on this model,the apparent permeability model of shale gas in shale core was established by equatng the core to a curved circular bundle with different radius,and the contribution of viscous flow,Knudsen diffusion and surface diffusion to apparent permeability were calculated. The influence of the distribution of different pore radius and the maximum pore radius on the apparent permeability were analyzed. The results showed that the effect of macropore on apparent permeability was much greater than that of micropore in the core. With the increase of the maximum pore radius,the apparent permeability between different pore distributions became smaller and smaller. Under the condition of low pressure or low pore radius,the effect of surface diffusion on apparent permeability should not be neglected. Compared with Knudsen diffusion and surface diffusion,the contribution of viscous flow in the shale core to apparent permeability was dominant under reservoir conditions,and the influence of surface diffusion could be ignored.
引文
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[2]蔡振华,廖新维,杜志强,等.煤层气排采时渗透率动态特征研究[J].河南理工大学学报(自然科学版),2014,33(2):149-153.CAI Z H,LIAO X W,DU Z Q,et al.Research method for dynamic permeability of coal bed methane reservoir[J].Journal of Henan Polytechnic University(Natural Science),2014,33(2):149-153.
[3]李国庆,孟召平,王保玉.高煤阶煤层气扩散-渗流机理及初期排采强度数值模拟[J].煤炭学报,2014,39(9):1919-1926.LI G Q,MENG Z P,WANG B Y.Diffusion and seepage mechanisms of high rank coal-bed methane reservoir and its numerical simulation at early drainagerate[J].Journal of China Coal Society,2014,39(9):1919-1926.
[4]CURTIS J B.Fractured shale:gas systems[J].AAPGBulletin,2002,86(11):1921-1938.
[5]张金川,金之均,袁明生.页岩气成藏机理和分布[J].天然气工业,2004,24(7):15-18.ZHANG J C,JIN Z J,YUAN M S.Reservoiring mechanism of shale gas and its distribution[J].Natural Gas Industry,2004,24(7):15-18.
[6]VIVEK SWAMI,CLARKSON C R,TONY SETTARIA.Non darcy flow in shale nanopores:Do we have a final answer[M].Calgary Canada:Socicty of Petroleum Engineers,2012.
[7]ALI BESKOK,GEORGE EM KARNIADAKIS.A model for flows in channels,pipes,and ducts at micro and nano scales[J].Microscale Thermophysical Engineering,1999,3:43-77.
[8]SARAH M,COOPER BRETT A,CRUDEN M,et al.Gas transport characteristics through a carbon nanotubule[J].Nano Letters,2004,4(2):377-381.
[9]FRANCOIS ANDRE FLORENCE,JAY RUSHING,KENT EDWARD NEWSHAM,et al.Improved permeability prediction relations for low permeability sands[C]//Denver:The 2007 SPE Rocky Mountain Oil&Gas Technology Symposium,2007.
[10]JAVADPOUR F.Nanopores and apparent permeability of gas flow in mudrocks(shales and siltstone)[J].Journal of Canadian Petroleum Technology,2009,48(8):16-21.
[11]FARUK CIVAN.Effective correlation of apparent gas permeability in tight porous media[J].Transport in Porous Media,2010,82(2):375-384.
[12]张艳玉,李冬冬,孙晓飞,等.实际状态下的页岩气表观渗透率计算新模型[J].天然气工业,2017,37(11):53-60.ZHANG Y Y,LI D D,SUN X F,et al.A new model for calculating the apparent permeability of shale gas in the real state[J].Natural Gas Industry,2017,37(11):53-60.
[13]ROBERT P,SUTTON.Fundamental PVT calculations for associated and gas/condensate natural-gas systems[J].SPE Reservoir Evaluation&Engineering,2007,10(3):270-284.
[14]DRANCHUK P M,ABOU-KASSEM H.Calculation of Z factors for natural gases using equations of state[J].Journal of Canadian Petroleum Technology,1975,14(3):34-36.
[15]秦积舜,李爱芬.油层物理学[M].东营:中国石油大学出版社,2006.QIN J S,LI A F.Petrophysics[M].Dongying:China U-niversity of Petroleum Press,2006.
[16]CHEN Y D,YANG R T.Concentration dependence of surface diffusion and zeolitic diffusion[J].AICh EJournal,1991,37(10):1579-1582.
[17]郭亮,彭晓峰,吴占松.甲烷在成型纳米活性炭中的吸附动力学特性[J].化工学报,2008,59(11):2726-2732.GUO L,PENG X F,WU Z S.Dynamical characteristics of methane adsorption on monolith nanometer activated carbon[J].Journal of Chemical Industry and Engineering,2008,59(11):2726-2732.
[18]DARABI H,ETTEHAD A,JAVADPOUR F,et al.Gas flow in ultra-tight shale strata[J].Journal of Fluid Mechanics,2012,710:641-658.
[19]WANG J,LIU H,WANG L,et al.Apparent permeability for gas transport in nanopores of organic shale reservoirs including multiple effects[J].International Journal of Coal Geology,2015,152:50-62.